The value of $$\left[ {5\frac{4}{9} \div {{\left( {\frac{{11}}{4} - \frac{{13}}{6}} \right)}^2}} \right] \div {\left[ {7\frac{3}{{11}}{\text{ of }}8\frac{4}{5} \div 1\frac{5}{7} - \frac{4}{3}} \right]^2}{\text{is:}}$$

Solution(By Examveda Team)

$$\eqalign{ & \left[ {5\frac{4}{9} \div {{\left( {\frac{{11}}{4} - \frac{{13}}{6}} \right)}^2}} \right] \div {\left[ {7\frac{3}{{11}}{\text{ of }}8\frac{4}{5} \div 1\frac{5}{7} - \frac{4}{3}} \right]^2} \cr & = \left[ {\frac{{49}}{9} \div {{\left( {\frac{{33 - 26}}{{12}}} \right)}^2}} \right] \div {\left[ {\frac{{80}}{{11}}{\text{ of }}\frac{{44}}{5} \div \frac{{12}}{7} - \frac{4}{3}} \right]^2} \cr & = \left[ {\frac{{49}}{9} \times \frac{{{{12}^2}}}{{49}}} \right] \div {\left[ {64 \times \frac{7}{{12}} - \frac{4}{3}} \right]^2} \cr & = \left[ {\frac{{49}}{9} \times \frac{{144}}{{49}}} \right] \div {\left[ {\frac{{112}}{3} - \frac{4}{3}} \right]^2} \cr & = \frac{{16 \times 3 \times 3}}{{108 \times 108}} \cr & = \frac{{16 \times 9}}{{108 \times 108}} \cr & = \frac{1}{{81}} \cr} $$